Let Q be an acute angle such that sinQ=.6. Find the values of the following using Trig Identities: cosQ and tanQ

sin^-1(.6) = 36.8 degrees

cos36.8 = .80
tan36.8 = .748

They probably wanted exact values without using a calculator.

given sinQ = .6 = 6/10 or 3/5
so Q is in a right angled triangle with opposite side of 3 and hypotenuse of 5.
You should recognize the famous 3-4-5 right-angled triangle.
then
cosQ = 4/5 or .8
tanQ = 3/4 or .75

these values are "exact"

You can do it this way:

sin^2 + cos^2=1
.36+cos^2=1
solve for cosTheta.
Then finally, tanTheta= sinTheta/CosTheta

your amazing.

To find the values of cosQ and tanQ, we can use the Pythagorean Identity and the definitions of cosine and tangent.

First, let's recall the Pythagorean Identity:
sin^2Q + cos^2Q = 1

Given that sinQ = 0.6, we can square both sides to find sin^2Q:
(sinQ)^2 = (0.6)^2
sin^2Q = 0.36

Now, substituting this value into the Pythagorean Identity, we have:
0.36 + cos^2Q = 1

To find the value of cosQ, we can subtract 0.36 from both sides and take the square root:
cos^2Q = 1 - 0.36
cos^2Q = 0.64

Taking the square root of both sides, we find:
cosQ = ±√0.64

Since Q is an acute angle, cosQ is positive. Therefore:
cosQ = √0.64
cosQ = 0.8

Now, to find the value of tanQ, we can use the definition of tangent:
tanQ = sinQ / cosQ

Substituting the given value of sinQ and the calculated value of cosQ, we have:
tanQ = 0.6 / 0.8
tanQ = 0.75

Therefore, the values of cosQ and tanQ are 0.8 and 0.75, respectively.